Approximately Counting Butterflies in Large Bipartite Graph Streams

Author(s):  
Rundong Li ◽  
Pinghui Wang ◽  
Peng Jia ◽  
Xiangliang Zhang ◽  
Junzhou Zhao ◽  
...  
2021 ◽  
Author(s):  
Ziyi Ma ◽  
Yuling Liu ◽  
Yikun Hu ◽  
Jianye Yang ◽  
Chubo Liu ◽  
...  

2018 ◽  
Vol 9 (12) ◽  
pp. 2147-2152
Author(s):  
V. Raju ◽  
M. Paruvatha vathana

10.37236/1748 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Nagi H. Nahas

The best lower bound known on the crossing number of the complete bipartite graph is : $$cr(K_{m,n}) \geq (1/5)(m)(m-1)\lfloor n/2 \rfloor \lfloor(n-1)/2\rfloor$$ In this paper we prove that: $$cr(K_{m,n}) \geq (1/5)m(m-1)\lfloor n/2 \rfloor \lfloor (n-1)/2 \rfloor + 9.9 \times 10^{-6} m^2n^2$$ for sufficiently large $m$ and $n$.


Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 925
Author(s):  
Michal Staš

The crossing number cr ( G ) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main goal of the paper is to state the crossing number of the join product K 2 , 3 + C n for the complete bipartite graph K 2 , 3 , where C n is the cycle on n vertices. In the proofs, the idea of a minimum number of crossings between two distinct configurations in the various forms of arithmetic means will be extended. Finally, adding one more edge to the graph K 2 , 3 , we also offer the crossing number of the join product of one other graph with the cycle C n .


Author(s):  
Jürgen Jost ◽  
Raffaella Mulas ◽  
Florentin Münch

AbstractWe offer a new method for proving that the maxima eigenvalue of the normalized graph Laplacian of a graph with n vertices is at least $$\frac{n+1}{n-1}$$ n + 1 n - 1 provided the graph is not complete and that equality is attained if and only if the complement graph is a single edge or a complete bipartite graph with both parts of size $$\frac{n-1}{2}$$ n - 1 2 . With the same method, we also prove a new lower bound to the largest eigenvalue in terms of the minimum vertex degree, provided this is at most $$\frac{n-1}{2}$$ n - 1 2 .


2021 ◽  
pp. 100093
Author(s):  
John D. Hogan ◽  
Jiandong Wu ◽  
Joshua A. Klein ◽  
Cheng Lin ◽  
Luis Carvalho ◽  
...  
Keyword(s):  

Author(s):  
Jie Cheng ◽  
Lu Lian ◽  
Zichen Xu ◽  
Dan Wu ◽  
Haoyang Zhu ◽  
...  

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